Question

The average number of accidents at controlled intersections per year is 5.2. Is this average a different number for intersections with cameras installed? The 68 randomly observed intersections with cameras installed had an average of 5.2 accidents per year and the standard deviation was 1.25. What can be concluded at the a-0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: H: 2 ? c. The test statistic ? Y (please show your answer to 3 decimal places.) d. The p-value- (Please show your answer to 4 decimal places.) e. The p-value is ? va f. Based on this, we should Select an answer the null hypothesis 8. Thus, the final conclusion is that ... The data suggest that the populaton mean is significantly different from 5.2 at a = 0.10, so there is statistically significant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is different from 5.2 accidents. The data suggest that the population mean is not significantly different from 5.2 ata=0.10,50 there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is different from 5.2 accidents The data suggest that the sample mean is not significantly different from 5.2 at & -0.10, so there is Statistically insignificant evidence to conclude that the sample mean number of accidents per year at intersections with cameras installed is different from 5.2 accidents. h. Interpret the p-value in the context of the study. If the population mean number of accidents per year at intersections with cameras installed is 52 and if another 68 intersections with cameras installed are observed then there would be a 100% chance that the population mean would either be less than 5 or greater than 5.2. If the population mean number of accidents per year at intersections with cameras installed is 5.2 and if another 68 intersections with cameras installed are observed then there would be a 100% chance that the sample mean for these 68 intersections with cameras installed would either be less than 5 or greater than 5.2. There is a 100% chance of a Type I error There is a 100% chance that the population mean number of accidents per year at intersections with cameras installed is not equal to 5.2. i. Interpret the level of significance in the context of the study If the population population mean number of accidents per year at intersections with cameras installed is different from 5.2 and if another 68 intersections with cameras installed are observed then there would be a 10% chance that we would end up falsely conceding that the population mean number of accidents per year at intersections with cameras installed is equal to 5.2. If the population mean number of accidents per year at intersections with cameras installed is 52 and if another 68 intersections with cameras installed are observed then there would be a 10% chance that we would end up falsely concuding that the population mean member of accidents per year at intersections with cameras installed is different from 5.2 There is a 10% chance that you will get in a car accident, so please wear a seat belt There is a 10% chance that the population mean number of accidents per year at intersections with

Answer 1

Note: Final answers are highlighted in colour.

a) As we dont know the population standard deviation, For this study we should use 1 sample t test.

b)The null and alternate hypothesis would be

H0: $\mu_0=5.2$

H1: $\mu_0\neq5.2$

c)

Test statistic= $\frac{\overline{X}-\mu_0}{S/\sqrt{n}}$ = $\frac{5.2-5.2}{1.25/\sqrt{68}}$ = 0

d)p value for t=0, degrees of freedom =67 is 1

e) The p value(1) is > $\alpha$ (0.1)

f)Based on this, we should not reject the null hypothesis.

g)Thus, the final conclusion is that.

The data suggest that the population mean is not significantly different from 5.2 at alpha= 0.10, so there is statistically insignificant evidence to conclude that the population mean number of accidents per year at intersections with cameras installed is different from 5.2 accidents. (Option 2)

h) I felt none of the options are correct

i)Level of significance is the probability of rejecting a correct null hypothesis. In the context of the current study,

If the population mean number of accidents per year at intersections with cameras installed is 5.2 and if another 68 intersections with cameras installed are observed then there would be a 10% chance that we would end up falsely concluding that the population mean number of accidents per year at intersections with cameras installed is different from 5.2 (Option 2)